Question on embedding of a metric space .

Question

State whether the statement below is true or false : For every metric space $(X,d)$ , there exists an isometric embedding of $X$ into $\mathbb{R}^4$ . Actually, the answer provided is false. I thought about the fact that there are obvious pairs of $(X,d)$ which satisfies the statement like discrete space and some other Euclidean spaces. But can't think of any non-trivial example to prove it false. On searching , I came through this : https://page-one.springer.com/pdf/preview/10.1007/BF01954540 Please provide me an example and please explain the terms "flat" and "dimensions" in Morgan's theorem a bit . Thanks in advance !!!